基于遗传算法的非线性方程组求解

针对目前求解非线性方程组所采用的牛顿法及其变形算法存在的运算量大、求解速度慢的问题,提出了一个求解非线性方程组近似解的通用遗传算法。该算法主要采用求解目标函数极小值的思想,并结合遗传算法并行搜索的特点,通过选择和设置适当的父体选择策略、杂交算子、变异算子等参数,使算法取得了较高的收敛速度和精度。实验结果表明,该方法明显优于传统方法,并具有运算速度快、精度高、通用性好的特点。     

基于混合遗传算法求解非线性方程组

将非线性方程组的求解问题转化为函数优化问题,且综合考虑了拟牛顿法和遗传算法各自的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了拟牛顿法的局部搜索、收敛速度快和遗传算法的群体搜索、全局收敛的优点。为了证明该混合遗传算法的有效性,选择了几个典型的非线性方程组,从实验计算结果、收敛可靠性指标对比不同算法进行分析。数值模拟实验表明,该混合遗传算法具有很高的精确性和收敛性,是求解非线性方程组的一种有效算法。     

基于自适应模拟退火遗传算法的非线性方程组求解

将非线性方程组的求解问题转化为函数的优化问题。针对传统的遗传算法（GA）容易早熟的不足,对其进行了两方面改进,采用自适应交叉比例产生交叉后代和变异后代,并融合模拟退火算法（SA）的思想,建立了自适应模拟退火遗传算法（ASAGA）。数值实验表明,该算法提高了遗传算法的全局搜索能力,是求解非线性方程组的一种有效算法。     

求解非线性方程组的蚁群算法

研究非线性方程组的求解问题,提高有效性。针对非线性方程数与变量数一致的非线性方程组问题,当方程组是一些强非线性方程组时,传统方法易导致失败,有效率低。为了提高求解强非线性方程组的求解效率,提出一种蚁群算法的求解方法。首先将方程组问题转化为函数优化问题,然后用全局搜索速度快的蚁群算法对函数进行求解,找到最优解,最后通过具体实例进行仿真研究,结果表明蚁群算法的有效性。     

基于禁忌搜索算法的VLSI布局

将禁忌搜索算法应用于VLSI门阵列的布局问题,建立了以总线长度和通道拥挤度的布局目标函数,用禁忌搜索算法求解目标函数的最小值,通过实验仿真,将本算法和遗传算法进行了比较,结果表明不论在解的质量和收敛速度方面,禁忌搜索算法优于遗传算法.     

基于混合遗传算法求解非线性方程组

将非线性方程组的求解问题转化为函数优化问题，且综合考虑了拟牛顿法和遗传算法各自的优点，提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了拟牛顿法的局部搜索、收敛速度快和遗传算法的群体搜索、全局收敛的优点。为了证明该混合遗传算法的有效性，选择了几个典型的非线性方程组，从实验计算结果、收敛可靠性指标对比不同算法进行分析。数值模拟实验表明，该混合遗传算法具有很高的精确性和收敛性，是求解非线性方程组的一种有效算法。     

基于极大熵差分进化混合算法求解非线性方程组*

针对非线性方程组,给出了一种新的算法——极大熵差分进化混合算法。首先把非线性方程组转换为一个不可微优化问题;然后用一个称之为凝聚函数的光滑函数直接代替不可微的极大值函数,从而可把非线性方程组的求解转换为无约束优化问题,利用差分进化算法对其进行求解。计算结果表明,该算法在求解的准确性和有效性均优于其他算法。     

基于区间—遗传算法求解非线性方程组

将非线性方程组的求解转化为函数优化问题,结合遗传算法的群体搜索、全局收敛的优点,及区间算法特有的解的存在性检验准则,提出了一种区间—遗传算法。在迭代计算过程中,区间算法为遗传算法搜索提供可靠区域,同时遗传算法为区间算法提供安全的初始区域。数值实验表明,该算法能够在较大范围的初始区间内快速,可靠地迭代得到高精度的区间解,是求解非线性方程组的一种有效的算法。     

基于微粒群优化的非线性方程组求解研究

在科学技术和工程应用中经常遇到求解非线性方程组的问题。提出了一种求解非线性方程组的通用数值方法。将非线性方程组的求解问题转化为函数优化问题,通过微粒群优化对其进行求解,最终得到非线性方程组较高精度的解。一系列测试实例显示了该算法在求解非线性方程组时具有简单性、高效性和普适性。     

求解一类凸优化问题的区间迭代算法

研究了一类非线性带约束的凸优化问题的求解.利用Kuhn-Tucker条件将凸优化问题等价地转化为多变元非线性方程组的求解问题.基于区间算术的包含原理及改进的Krawczyk区间迭代算法,提出一个求解凸优化问题的区间算法.对于目标函数和约束函数可微的凸优化,所提算法具有全局寻优的特性.在数值实验方面,与遗传算法、模式搜索法、模拟退火法及数学软件内置的求解器进行了比较,结果表明所提算法就此类凸优化问题能找到较多且误差较小的全局最优点.     

Optimal estimation of parameters of dynamical systems by neural network collocation method

In this paper we propose a new method to estimate parameters of a dynamical system from observation data on the basis of a neural network collocation method. We construct an object function consisting of squared residuals of dynamical model equations at collocation points and squared deviations of the observations from their corresponding computed values. The neural network is then trained by optimizing the object function.The proposed method is demonstrated by performing several numerical experiments for the optimal estimates of parameters for two different nonlinear systems. Firstly, we consider the weakly and highly nonlinear cases of the Lorenz model and apply the method to estimate the optimum values of parameters for the two cases under various conditions. Then we apply it to estimate the parameters of one-dimensional oscillator with nonlinear damping and restoring terms representing the nonlinear ship roll motion under various conditions. Satisfactory results have been obtained for both the problems.     

Modeling and control of two constrained manipulators

The coordinated control of two manipulators in the presence of environment constraints is studied in this paper. Such a control method is needed in applications in which the two manipulators grasp a common object whose motion is constrained by environments. The two manipulators are not only constrained with each other, but also constrained by the environment in their workspace. It is realized that the motion and constraint equations obtained directly from mechanics are not suitable for the control purpose. A set of equivalent equations are derived, which are in the standard form of the nonlinear system representation with clear state equations and output equations. A nonlinear feedback is found which exactly linearizes and decouples the dynamic nonlinear system of the two constrained manipulators. The coordinated controller design is then carried out based on the linearized system by using linear system theory.     

Computer-aided solution of some problems relating to control of the complicated mechanical systems

Consideration was given to control of a complex object whose motion obeys a multivariable nonlinear nonstationary mathematical model. Rigid constraints were imposed on the object’s dynamic precision. The paper considered computer-aided generation of the current equations of object motion with regard for the actuators which differ from subsystem to subsystem. The object is controlled adaptively with regard for the computer-based realization. The algorithms of control system operation that maintain the guaranteed precision of object motion were constructed. Conditions for problem solvability were formulated. The freeflying space robot was discussed by way of example.     

Methodology for generating continuous prediction equations for pulmonary function measures

A mathematical procedure is described for fitting piecewise linear equations constrained to join at estimable multiple junctions or breakpoints. The model parameters, a combination of both linear and nonlinear, are estimated using a "Separable Least Squares" algorithm. In this algorithm the linear parameters, estimated using the General Linear Model, are nested within the iterations of a nonlinear optimization routine. This formulation allows additional covariates to be included in the model and can be easily expanded to include any number of line segments, both linear and nonlinear. The procedure is demonstrated by estimating continuous lung function reference equations for healthy normal subjects. Comparison of these reference equations with previously published equations derived for the same subjects, illustrates the advantages of having continuous equations throughout the age range of the data.     

Wilson-Cowan neural-network model in image processing

The neural-network model based on the theory proposed by Wilson and Cowan has been simulated by using digitized real images. Mathematically, the model is based on coupled nonlinear differential equations that describe the functional dynamics of cortical nervous tissue, and the model can operate in different dynamical modes, depending on coupling strengths. The model is shown to store images in reduced form and to recognize edges of an object. Examples of how the network processes input images are shown.     

Applications of nonlinear Volterra equations of the first kind to the control problem for heat exchange dynamics

We consider a class of nonlinear integral Volterra equations of the first kind related to the automatic control problem for a nonlinear dynamical system (object) which is a black box with vector input and no output feedback. The characteristic features of the algorithms are illustrated on the example of mathematical modeling for nonlinear heat exchange processes.     

利用调制函数法的模糊模型参数辨识

利用调制函数法辨识非线性连续系统的模糊模型参数.系统的动力学微分方程存在微分项,通过输入输出数据辨识模糊模型参数时不能忽略扰动的影响,因此辨识模糊模型参数比较困难.利用调制函数法可以消除微分项,通过无微分项的联立方程的求解容易进行模糊模型参数辨识.几个非线性连续系统的仿真实验验证了所设计的利用调制函数法的模糊模型参数辨识的正确性和有效性.     

求解非线性方程组的量子行为粒子群算法*

介绍了利用量子行为粒子群算法解决非线性方程组的问题。求方程组的解归结为一个最优化问题,当方程组有多个解时,它的适应值函数就是具有多个最优解的多峰函数。为此,引进一种物种形成原理算法,该算法根据群体微粒的相似度并行地分成子群体。每个子群体是围绕一个群体种子而建立的。对每个子群体进行QPSO最优搜索,从而保证方程组中每个可能的解都能被搜索到,具有良好的局部寻优特性。对几个重要的测试函数进行仿真实验,结果证明了所用算法可以保证找到方程组所有的解,并且具有很好的精确度。     

The correntropy MACE filter

The minimum average correlation energy (MACE) filter is well known for object recognition. This paper proposes a nonlinear extension to the MACE filter using the recently introduced correntropy function. Correntropy is a positive definite function that generalizes the concept of correlation by utilizing second and higher order moments of the signal statistics. Because of its positive definite nature, correntropy induces a new reproducing kernel Hilbert space (RKHS). Taking advantage of the linear structure of the RKHS it is possible to formulate the MACE filter equations in the RKHS induced by correntropy and obtained an approximate solution. Due to the nonlinear relation between the feature space and the input space, the correntropy MACE (CMACE) can potentially improve upon the MACE performance while preserving the shift-invariant property (additional computation for all shifts will be required in the CMACE). To alleviate the computation complexity of the solution, this paper also presents the fast CMACE using the fast Gauss transform (FGT). We apply the CMACE filter to the MSTAR public release synthetic aperture radar (SAR) data set as well as PIE database of human faces and show that the proposed method exhibits better distortion tolerance and outperforms the linear MACE in both generalization and rejection abilities.     

求解非线性方程组的量子行为粒子群算法

介绍了利用量子行为粒子群算法解决非线性方程组的问题.求方程组的解归结为一个最优化问题,当方程组有多个解时,它的适应值函数就是具有多个最优解的多峰函数.为此,引进一种物种形成原理算法,该算法根据群体微粒的相似度并行地分成子群体.每个子群体是围绕一个群体种子而建立的.对每个子群体进行QPSO最优搜索,从而保证方程组中每个可能的解都能被搜索到,具有良好的局部寻优特性.对几个重要的测试函数进行仿真实验,结果证明了所用算法可以保证找到方程组所有的解,并且具有很好的精确度.